Republican congressional leaders opened some room Sunday for a longer-term deficit reduction agreement that eventually could blunt the effects of the $85 billion in automatic spending cuts now in place.

But in appearances on the Sunday talk shows, Speaker John A. Boehner, R-Ohio, and Senate Minority Leader Mitch McConnell, R-Ky., insisted that any revenue from a tax overhaul would have to be reserved for reducing tax rates and not used to fund government spending or lower the deficit.

The leaders appeared determined to keep the level of spending cuts in place but signaled that a longer-term deal to lower the deficit, overhaul the tax code and rein in spending on entitlement programs could still be had.

McConnell said on CNN’s “State of the Union” that Republicans are “open to discussing how to reconfigure those spending reductions without raising taxes.”

Boehner pointed the way forward in saying the House this week will pass a continuing resolution to extend government spending through the end of fiscal 2013 — the current six-month spending law (PL 112-175) expires March 27 — and then turn to drafting a fiscal 2014 budget resolution. He urged Senate Democrats to carry out their pledge to also adopt a budget blueprint.

“And out of that discussion and out of that process, maybe we can find a way to deal with our long-term spending problem,” Boehner said on “Meet the Press.”

Republicans, however, appear divided over whether revenue has to be set aside only for lowering tax rates. Some Republicans indicated in interviews Sunday that they may be open, as part of a broad deficit reduction deal, to consider using revenue to lower the deficit, to ease the effects of the spending cuts as well as to reduce tax rates as part of any tax overhaul.

New Hampshire Republican Sen. Kelly Ayotte said in an appearance on “This Week” that she would be willing to consider revenue increases to be applied to the debt if a tax overhaul is done to lower tax rates and the president considers an entitlement overhaul.

Republican Sens. John McCain of Arizona and Lindsey Graham of South Carolina said on “Face the Nation” that they want talks to resume between Congress and the White House to reach a grand bargain to reduce spending and deal with the deficit.

Graham said President Barack Obama and Boehner should pick up where they left off in last year’s deficit reduction talks with Republicans offering $600 billion in revenue through a tax overhaul and use that money to lower the deficit, rein in the cost of entitlement programs and find a way to substitute the automatic spending cuts. He also indicated some flexibility on tax increases.

“I’m not going to do any more small deals. I’m not going to raise taxes to fix sequestration. We don’t need to raise taxes to fund the government. We need to raise taxes to get our nation out of debt,” Graham said. “We can do the big deal if we have some leadership.”

Obama reached out by phone over the weekend to congressional Republicans who might be open to jump-starting talks that would have revenue and spending reductions on the table.

But McConnell said he has seen no evidence that Obama is making any inroads with Republicans who may be open to using increased revenue to soften the effects of the automatic spending cuts.

“I haven’t heard a single Senate Republican say they would be willing to raise a dime in taxes to turn off the sequester,” McConnell said. “The president is free to call whoever he chooses to. He doesn’t have to go through the speaker and myself to talk to our members.”

Boehner charged that the Obama administration had failed to offer any workable proposal to end the sequester and reiterated his position that the House has twice passed bills that would have replaced the first year of the spending cuts with longer-term reductions in mandatory spending.

“That’s just nonsense,” Boehner said of any serious White House efforts. “If he had a plan, why wouldn’t Senate Democrats go ahead and pass it?”

“The House passed a bill. The Senate can pass a bill. If we disagree, we go to conference and work it out,” Boehner added.

Boehner said Obama “got his tax hikes” when the payroll tax cut expired at the beginning of the year and when Congress enacted $600 billion in additional tax increases in the agreement reached to avert the fiscal cliff (PL 112-240). Going forward, the Ohio Republican said, any changes to the tax code should be focused on lowering tax rates. “We have to deal with the spending side just like every American family has to,” Boehner said.

There was one point on which all parties seemed to agree Sunday: that the House and Senate would act on a bipartisan basis to quickly pass the continuing resolution to avoid government shutdown.

White House National Economic Council Director Gene Sperling appeared on “Meet the Press” and “State of the Union” with a laminated copy of the president’s economic talking points and repeatedly emphasized that nonpartisan economists estimate the sequester will eliminate about 750,000 jobs and reduce the gross national product by 0.6 percent this year.

He said the Senate will take up this week a measure to give the administration more flexibility in dealing with the automatic spending cuts that are the first installment of about $1.2 trillion in deficit reduction over the next 9 years under the 2011 debt increase law (PL 112-25).

Sperling cast that step as a temporary one needed before any longer-term deficit package could be worked out.

“I want you to know the president is doing everything he can. He brought the Republican and Democratic leadership in on Friday,” Sperling said. “Saturday afternoon, the president was working the phone talking to both Democrats and Republicans who he thought were willing to be part of the type of bipartisan compromise that we need to get out of this.”